AURANGABAD, India—Conservative Hindu activist Chetna Sharma looked sternly at her audience of more than 40 young Hindu women gathered in the living room of a rural home and issued a warning: Muslim men would try to trick them into marriage and force them to convert to Islam.

Given a chance, Muslim men would force a woman "to have two or three children and then leave her, or rape her, or throw acid on her if she resists, or murder her," she said. "You can't even imagine what can happen if you don't protect yourself...